(x+5)(x)=72

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Solution for (x+5)(x)=72 equation: 


Simplifying
(x + 5)(x) = 72

Reorder the terms:
(5 + x)(x) = 72

Reorder the terms for easier multiplication:
x(5 + x) = 72
(5 * x + x * x) = 72
(5x + x2) = 72

Solving
5x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + 5x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 5x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 5x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 5x + x2 = 0 + 72
5x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
5x + x2 = 72

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 72 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 72 + 6.25

Combine like terms: 72 + 6.25 = 78.25
6.25 + 5x + x2 = 78.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
x + 2.5 = 8.845903006

Simplifying
x + 2.5 = 8.845903006

Reorder the terms:
2.5 + x = 8.845903006

Solving
2.5 + x = 8.845903006

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 8.845903006 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8.845903006 + -2.5
x = 8.845903006 + -2.5

Combine like terms: 8.845903006 + -2.5 = 6.345903006
x = 6.345903006

Simplifying
x = 6.345903006


Subproblem 2
x + 2.5 = -8.845903006

Simplifying
x + 2.5 = -8.845903006

Reorder the terms:
2.5 + x = -8.845903006

Solving
2.5 + x = -8.845903006

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -8.845903006 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8.845903006 + -2.5
x = -8.845903006 + -2.5

Combine like terms: -8.845903006 + -2.5 = -11.345903006
x = -11.345903006

Simplifying
x = -11.345903006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.345903006, -11.345903006}

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